Luck's first career playoff victory sends Indianapolis (12-5) to either Denver or New England next weekend for the divisional round with four straight wins.

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The Chiefs took a 38-10 lead early in the third quarter, but all they could muster after that was two field goals, while Luck and the Colts began their comeback.

The Indianapolis Colts had all the Luck — at least once the second half started.

Andrew Luck threw three touchdown passes after halftime, including a 64-yarder to a wide-open T.Y. Hilton for the go-ahead score with 4:22 left, leading the Colts from a four-TD deficit to an improbable 45-44 comeback victory over the Kansas City Chiefs in a wild-card game Saturday.

Indianapolis (12-5) became only the second team in playoff history to win after trailing by 28 or more points, according to STATS. The other: Buffalo over Houston 41-38 in overtime in January 1993. The Colts will travel to either Denver or New England next weekend for the divisional round with four straight wins.

Luck was an incredible mix of good and bad, finishing 29 of 45 for 443 yards, the second-highest total in franchise history for a playoff game, with four TDs and three interceptions. He also picked up a fumble and ran it in for a 5-yard score when the loose ball bounced back to him.

2014 NFL Playoffs

"We never panicked," Luck said. "We took it one play at a time."

Hilton broke a franchise playoff record with 13 catches and 224 yards, finishing with two TDs — including the winner.

Kansas City (11-6) finished its turnaround season with three straight losses, two to the Colts and an eighth straight postseason defeat — none more stunning than this one. The eight straight losses broke a tie with the Detroit Lions for the longest playoff skid.

Alex Smith was 30 of 46 for 378 yards with four TDs and no interceptions on a day he lost his top two running backs, Jamaal Charles and Knile Davis, and starting receiver Donnie Avery to injuries.

But Luck got the last word with his jaw-dropping rally.

Things appeared bleak with Indy trailing 31-10 at halftime, and they looked even worse when Luck's first pass of the second half was picked off and returned to the Indy 18. Three plays later, Smith threw a 10-yard TD pass to Davis to make it 38-10 with 13:39 left in the third quarter.

As it turned out, Luck had plenty of time to turn things around. In a big way.

With Indy in its no-huddle offense and nothing to lose, Luck started throwing the ball over the field, and Donald Brown's 10-yard TD run made it 38-17.

Then, Luck converted a lost fumble by Smith into a 3-yard TD pass to Brown. Suddenly, it was 38-24 and the fans who were booing at halftime were in a frenzy.

The noise subsided briefly after the Chiefs turned Luck's third interception into a 42-yard field goal, but Luck answered with a 12-yard TD pass to cut the deficit to 41-31 after three quarters.

Luck was just getting started.

Eric Berry's hit jarred the ball loose from Brown near the goal line early in the fourth, but the ball bounced right into Luck's hands and he picked it up and squirted through the middle for to make it 41-38 with 10:38 to go.

Kansas City drove for another field goal, but this time with Kansas City linebacker Justin Houston out of the game with knee injury, Hilton broke free down the middle of the field and Luck hit him in stride behind the secondary for the 64-yard score that made it 45-44.

All the Colts had to do then was stop Kansas City on downs, and kneel down three times.